Page 68 - Close Combat
In the short introduction to 'Close Combat', the second paragraph states that a move is required to stand up when standing is identified as a free action on page 66.
Extract from page 68: To attack an opponent in close combat, you need to be standing on your feet. If you are prone, you must first use a move to get up.
Standing or dropping are free actions done as a part of your move. They are not independent free actions. So you can't stand up, attack, and then move. It's either stand up and immediately move, or stand up and don't move at all on your turn.
Page 71 - Critical Injuries
In the second paragraph, it states in the brackets that you require two or more successes for a critical injury. Earlier on page 68, it says that you need to roll two successes more than your opponent. This may be as the reference on page 68 is related to an opposed roll but page 71 simply states that you just need two eye symbols.
In Close Combat, other than Free Attacks, you're attacks are opposed by your target. So you can only hit him if you get more successes than him, and you can only get a crit if you get 2+ successes more than him.